Propagation of sound waves
(A) Source of sound wave
Sound is a form of wave motion which is conveyed through an elastic medium from a vibrating body to a listener.
Sound produced by sources is a longitudinal wave; that is, it is a form of energy which moves in such a way that its direction of motion is parallel to the direction of oscillation of the molecules of the medium. The study of sound waves is very important, because we make use of sound in our everyday life.
(B) Transmission of sound waves
An electric Bell is suspended inside an airtight jar as shown below. The jar is connected to a vacuum pump. Then the electric Bell is then operated and set ringing. As air is gradually pumped out from the jar, it is observed that the sound from the bell gets fainter and fainter though the hammer is still striking the bell.
Therefore no sound is heard even when all the air in the jar is evacuated.
Experiment showing that a material medium is always required to propagate sound. Sound waves do not travel through a vacuum.
(C)The speed of sound waves
The speed of sound is found to depend on the density and elasticity of the medium, which means that the speed varies from medium to medium.
Reflection of sound (echoes): a sound heard after the reflection of sound waves from a plane surface is called an echo. Echo can be used to determine speed of sound in air, by directing a sound signal to a wall and measuring the time taken by the echo produced to reach us.
A sound Velocity probe used to measuring sound in water
Note that stopwatch is used to measure sound echoes on land. For example, by means of a stopwatch held by a second person, a number of successive claps are timed and hence, the time between successive claps is found.
V= 2x ms-1/t
t= seconds, x= distance, v= speed of the sound wave.
To calculate speed of sound wave in water
x= echo depth of the sea
It is usually studied in a large hall. The sounds are being reflected by walks, roof, and floor of the hall. It takes time for the sound to die away. Reverberation causes disorder or confusion when assimilating sound especially in a music hall, so it can be corrected or reduced by using soft furnishing and padding of the walls of the hall.
Limit of audibility: the general limit are ranged from 4000Hz to about 20kHz
- Beat: beat is a phenomenon obtained when two notes of nearly equal frequency are sounded together.
- Doppler effect in sound :it is the change in frequency or pitch of a source when there is a relative motion between the source and the observer. It occurs in both sound and light waves.
(E) Formula for apparent frequency
F ‘= (v+v0 /v-vs)
When source S is moving towards a stationary observer O f ‘=(v / v+vs) f
The relative velocity between S and O is V+Vs
When source S, is stationary and observer O moving towards it. If V0 is the Velocity of the observer then the relative velocity in this case between sound and observer is V+V0. So f ‘= (V-V0 / V) f
(F) Characteristics of sounds
- Pitch is the characteristic of a note which enables us to differentiate a high note from a low one.
- Quality of a note is the characteristics that distinguishes it from another note of the same pitch and loudness when played on musical instruments.
- Intensity and loudness: intensity of sound at a certain place is the rate of flow of energy per unit area perpendicular to the direction of the sound wave, while loudness is a sensation in the mind of the individual observer, depending on the intensity of sound.
(G)Modes of vibration of a stretched string (the sonometer)
Sonometer is a hollow box on which a string or wire is stretched as shown above.
The vibrating length of a sonometer l= ∆/2
Note: fundamental frequency is written as f0 = 1/2L √T/m where m= mass, T=tension, as l = length.
Vibration in stretched string
(H) Vibration of air column in pipes
The study of Modes of vibrations in pipes is of importance because musical instruments such as flutes, drums, etc, are either open or closed pipes. A closed pipe is one which is closed at one end only but an open pipe is one which is open at both ends.
Overtones of a closed pipes
Vibrations in an open pipe
(I) Musical instruments
Most musical instruments which familiar with can be classified as follows:
- String instruments; examples are the sonometer, the guitar, the piano and the violin.
- Wind instruments; examples flutes, clarinets, saxophones, trumpet, etc.
- Percussion instruments; examples bells, drums, and tuning forks.
1.A man standing 300m away from a wall sounds a whistle. The echo from the wall reaches him 1.8s later. Calculate the Velocity of sound in air? (Wassce 1991)
Solution: x= vt/2; 2d= vt; v= 2d/t = 2×330/1.8
6660/1.8 = 1110/3 = 333.3m/s
2. Which of the following instruments produces sound by the vibration of air column? (Wassce 1998)
3. The pitch of a note is not affected by? (Wassce 2018)
B. Tension in a vibrating string
C. Mass of a vibrating string
D. Amplitude of sound wave
Solution: The pitch of a note is not affected by the amplitude of the sound wave.
4. A note of frequency 2000Hz has a Velocity of 400m/s. Calculate the wavelength of the note. (Wassce 2006)
Solution: V= f∆; ∆= v/f= 400/2000 = 0.2m
5. The note produced by a string has a fundamental frequency of 400Hz. If the length of the string is doubled while the tension in the string is increased by a factor of 4, the frequency is? (Jamb 1994)
Solution: f= 1/2L √T/m; T2= 4T1, L2= 2L1
2f1L1 / 2f2L2 = √T1 / T2; 400×L1 / f×2L1 = √T1/ 4T1; f= 400Hz
6. The quality (timbre) of sound depends on? ( Jamb 1981)
7. If the fundamental frequency of a closed pipe organ on a day when the speed of sound is 340m/s is 170Hz, , then the length of the pipe is ? (Jamb 1985)
Answer: ∆= v/f = 340/170 = 2m; for closed pipe
L= 1/4∆ = 1/4 × 2/1 = 0.5m= 50cm
8. Which of the following is true of light and sound waves? (Jamb 1991)
A. They both transmit energy
B. They both need a medium for propagation
C. They are both transverse waves
D. Their Velocities in air are equal